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TitleCombinatorial-topological framework for the analysis of global dynamics
Author(s)Bush, Justin
Gameiro, Marcio
Harker, Shaun
Kokubu, Hiroshi
Mischaikow, Konstantin
Obayashi, Ippei
Pilarczyk, Pawel
KeywordsDynamical system
Morse decomposition
Conley index
Grid decomposition
Graph algorithms
Rigorous numerics
Issue date26-Apr-2012
PublisherAIP Publishing
Abstract(s)We discuss an algorithmic framework based on e cient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.
ISSN1054-1500 (print)
1089-7682 (online)
AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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